Theme Essential Question: How does the probability of an outcome affect the decision making process in real-life situations?
Essential Questions: How can you find the theoretical probability of an event?
Standards:
7. SP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
7. SP.7a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
Objectives:
The student will explore and analyze theoretical probability.
The student will calculate theoretical probability.
The student will make prediction basic on their probability.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team Teachers should be flexible as they develop theoretical and experimental probability to assure students understand the differences and similarities of this concept.
Background Information Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 Students learn to make predictions about the relative frequency of an event by using simulations to collect, record, organize and analyze data. Students also develop the understanding that the more the simulation for an event is repeated, the closer the experimental probability approaches the theoretical probability. Recommended: For a quick overview of the stands(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/.
Assessment: Product This project will encompass the theoretical and experimental probability units. Students will be designing and developing a hands-on presentation using physical objects, graphing calculators, or web based simulations.
Students are to work as partners or small group to design and develop a simulation.
Students are to calculate the theoretical probability of their simulation. (week 2)
Students are to analyze and make predictions based on their simulation. (week 2)
Students are to collect data using physical objects, graphing calculators, or web based simulation. They are to calculate the experimental probability of their simulation. (week 3)
Students are to compare the results of their theoretical and experimental probability and develop a viable argument. (week 3)
Key Questions
What is theoretical probability?
How is theoretical probability used in making generalized predictions?
Observable Student Behaviors (Performance)
The student can successfully calculate, analyze and make predictions based on theoretical probability.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary:
Math
Theoretical probability P(event) = Number of ways the event can occur_ Total number of equally likely outcomes
Suggested Activities:
Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 7-2, p. 161-164
v Gizmo Correlation
7.SP.6
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
7.SP.7
Probability Simulations
Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
v NCTM Illuminations http://illuminations.nctm.org/LessonDetail.aspx?ID=L448 Students explore the relationship between theoretical and experimental probabilities using an interactive tool known as a "box model." A "box model" is a statistical device that can be used to simulate standard probability experiments such as flipping a coin or rolling a die.
High Recommended: Non Available
Glencoe 7th Grade Mathematics Application and Concepts Course 2, Chapter 9-6, p. 393-397
Teaching the Common Core Math Standards with Hands-On Activities,
This lesson activity allows students to explore probability through the use of spinners, dice, and a random image chooser. Students will discuss if a situation has a equal probability or unequal probability.
7S.P 7a Introduction to Probability
Introduces probablility, experimental and theorectical probability, complementary events.
Content: Theoretical Probability
Dates: 4/15/2013 - 4/19/2013
Theme Essential Question:
How does the probability of an outcome affect the decision making process in real-life situations?
Essential Questions:
How can you find the theoretical probability of an event?
Standards:
Objectives:
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team
Teachers should be flexible as they develop theoretical and experimental probability to assure students understand the differences and similarities of this concept.
Background Information
Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011
Students learn to make predictions about the relative frequency of an event by using simulations to collect, record, organize and analyze data. Students also develop the understanding that the more the simulation for an event is repeated, the closer the experimental probability approaches the theoretical probability.
Recommended: For a quick overview of the stands(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/.
Assessment:
Product
This project will encompass the theoretical and experimental probability units. Students will be designing and developing a hands-on presentation using physical objects, graphing calculators, or web based simulations.
Key Questions
Observable Student Behaviors (Performance)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary:
Total number of equally likely outcomes
Suggested Activities:
- Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 7-2, p. 161-164
v Gizmo Correlation- 7.SP.6
- Theoretical and Experimental Probability
- Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
- 7.SP.7
- Probability Simulations
- Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
v NCTM Illuminationshttp://illuminations.nctm.org/LessonDetail.aspx?ID=L448
Students explore the relationship between theoretical and experimental probabilities using an interactive tool known as a "box model." A "box model" is a statistical device that can be used to simulate standard probability experiments such as flipping a coin or rolling a die.
Diverse Learners
Homework: (Teacher Discretion)
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- 7S.P 7 Exploring Probability
This lesson activity allows students to explore probability through the use of spinners, dice, and a random image chooser. Students will discuss if a situation has a equal probability or unequal probability.- 7S.P 7a Introduction to Probability
Introduces probablility, experimental and theorectical probability, complementary events.Other Activities, etc.
Language
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Week 2
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Week 4
Week 5
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7 Matrix
Accelerated 7
Matrix
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Week 2
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Week 4
Week 5
Week 6
Home K-2
Home 3-6
Home 6-8
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Unit 3
Unit 4
Unit 5
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